You could feed the Weasel food until it trusts you, then put it in your Backpack forever.

You get another animal that is bigger then it.Such as a bear or wolf and feed the weasal
to that animal.If you havent unlocked those animals yet then the best idea would be to
gain its trust and keep it in your backpack.Or keep an eye on it and when it goes to eat
something you dont want it to pick it up and move it away.This also gains you trust for
the animal you saved.

keep it in yor bakpak forever

Maybe you can earn it's trust and put it in your backpack. and when you unlock the wolf or
the bear, you can feed the weasel to the animal. Good Luck!:)

Also, if it seems too late and already caught an animal and is having a fight with it, I
found out you can stick your hand into the cloud (not literally) and press B in front of
the dust cloud and you can pull out an animal. Either animal works, the weasel will be mad
but you can toss it away to put the animal in your backpack or just....*shrugs*

Hope I helped!

Well get it happy and put it in your backpack. Make it mad and it*ll move out. Get an
animal (like a bear) and make the animal eat the weasel. Or wait for the weasel to retire.
Lol